A Class Of Markovian Jump Nonlinear Robust H_∞ Fuzzy Control

Markovian jump system is a switching system, whose structure and parameters varystochastically. Compared with regular switched system and piecewise-linear system, Marko-vian jump systems have a more richer structure and parameters’ variations, therefore,many physical processes in practice can be modeled as Markovian jump systems. Becauseof the fact that the uncertainties and delay are the sources of instability and performancedeterioration, recently, the problems of robust stability and H∞control with parameteruncertainty and delay are a main research direction of systems theory, and many quite com-plete theory interesting criteria have been derived. Usually, it is assumed that the delay istime-invarying or delay information is from0to an upper bound. But, in many practicalapplications,the delay is time-varying for most of the real systems and delay information isfrom an low bound to an upper bound. In this thesis, we focus upon the problem of robustH∞fuzzy control for a class of uncertain continuous-time nonlinear Markovian jump systemswith time-varying delay which can be represented by the T-S fuzzy model. The main resultsare as follows:1) Robust H∞performance analysis for nonlinear Markovian jump system with uncertainparameters and time-varying delay.In this part, The problem of robustly stochastically stable for nonlinear Markovianjump system with a prescribed H∞performance of disturbance attenuation for all admissi-ble parameter uncertainties is investigated, and the considered uncertainties are parameteruncertainties and the parameter is norm-bounded. In order to obtain a less conservativecontrol design, a new stochastic Lyapunov-Krasovskii function is constructed by modifyingthe delay information. Finally, the provided example demonstrates the efectiveness of themain sufcient conditions.2) Robust H∞fuzzy control for nonlinear Markovian jump systems with uncertain pa-rameters and time-varying delay.In this section,we extend the previous results of performance analysis to Robust H∞fuzzy control design for the uncertain Markovian jump fuzzy systems. This study provides anLMI-based sufcient condition for the existence of fuzzy controller such that the closed-loopsystem is robustly stochastically stable with a prescribed level of disturbance attenuation.Finally, we show the feasibility and validity of the developed results by an example.